Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-8y &= 4 \\ x-3y &= 1\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {3y+1}$ Substitute this expression for $x$ in the first equation. $-({3y + 1}) - 8y = 4$ $-3y - 1 - 8y = 4$ Simplify by combining terms, then solve for $y$ $-11y - 1 = 4$ $-11y = 5$ $y = -\dfrac{5}{11}$ Substitute $-\dfrac{5}{11}$ for $y$ in the top equation. $-x-8( -\dfrac{5}{11}) = 4$ $-x+\dfrac{40}{11} = 4$ $-x = \dfrac{4}{11}$ $x = -\dfrac{4}{11}$ The solution is $\enspace x = -\dfrac{4}{11}, \enspace y = -\dfrac{5}{11}$.